The letter said: "We should celebrate the fact that we are all living longer lives, particularly disabled people and those with long-term conditions.

"But the unavoidable challenge we face is how to support the increasing number of people who need care.

"It is currently a challenge which we are failing to meet - resulting in terrible examples of abuse and neglect in parts of the care system.

"This comes at huge cost to the dignity and independence of older and disabled people, but also to our society, family life and the economy."

'At risk'

The letter went on to say people were being left "lonely, isolated and at risk" because of the problems with the current system.

It cited research produced by Age UK which suggested that of the 2m people with care needs, 800,000 were not getting any support because councils had started restricting access to services.

In a separate interview with the BBC, Councillor David Rogers of the Local Government Association said councils, which are in control of running the means-tested system, are united in their view of the need for change.

He said: "There is no doubt about the urgency and need for reform. Without exception, across local government all parties are in agreement. National politicians must try to come up with something."

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Media captionChair of the Care and Support Alliance Simon Gillespie: ''The current system is broken''

Attempts to reform the system collapsed before the last election after cross-party talks failed.

Labour accused the Tories of dirty tricks after they launched a campaign suggesting Mr Burnham, who was then health secretary, wanted to introduce a death tax to pay for changes to the system.

Once again, the way any new system is paid for is expected to be the most controversial and difficult element of the discussions.

Last summer a government-commissioned review by the economist Andrew Dilnot recommended a partnership between the state and individual with people responsible for the first £35,000 of their social care costs and the government picking up the bill after that.

But questions still remain over how affordable this is for both parties.

The government refused to comment on the upcoming talks, but Mr Burstow said ministers saw reform of social care as an "urgent priority".

Mr Burnham added reforming social care was the "biggest public policy challenge the country faces".

"This is an issue that transcends party politics and we look forward to playing our part in any discussions."